Apparatus and method for electrical stimulation of human neurons

ABSTRACT

An apparatus and method for retinal stimulation are shown. The method comprises varied parameters, including frequency, pulse width, and pattern of pulse trains to determine a stimulation pattern and neural perception threshold, and creating a model based on the neural perception thresholds to optimize patterns of neural stimulation.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. application Ser. No.11/818,373 filed Jun. 14, 2007 for A Method for Stimulation of the HumanRetina Using Pulse Trains, which claims priority to U.S. ProvisionalSer. No. 60/814,308 for “Human Retinal Electrical Stimulation UsingPulse Trains” filed on Jun. 16, 2006, U.S. Provisional Ser. No.60/872,098 for “Evidence For Synchrony Using Direct ElectricalStimulation Of The Human Retina” filed on Dec. 1, 2006; U.S. ProvisionalSer. No. 60/872,099 for “A Model Of Temporal Integration DuringElectrical Stimulation Of The Human Retina” filed on Dec. 1, 2006; U.S.Provisional Ser. No. 60,872,101 for “Selective Adaptation UsingElectrical Stimulation In Humans” filed on Dec. 1, 2006; and U.S.Provisional Ser. No. 60/873,208 for “A Model Of Temporal IntegrationDuring Electrical Stimulation Of The Human Retina” filed on Dec. 6,2006, all of which are incorporated herein by reference in theirentirety.

GOVERNMENT RIGHTS NOTICE

This invention was made with government support under grant No.R24EY12893-01, awarded by the National Institutes of Health. Thegovernment has certain rights in the invention.

FIELD

The present disclosure is generally directed to neural stimulation andmore specifically to an apparatus and method for providing intensitycontrol.

BACKGROUND

As intraocular surgical techniques have advanced, it has become possibleto apply stimulation on small groups and even on individual retinalcells to generate focused phosphenes through devices implanted withinthe eye itself. This has sparked renewed interest in developing methodsand apparatuses to aid the visually impaired. Specifically, great efforthas been expended in the area of intraocular retinal prosthesis devicesin an effort to restore vision in cases where blindness is caused byphotoreceptor degenerative retinal diseases such as retinitis pigmentosaand age related macular degeneration which affect millions of peopleworldwide.

Neural tissue can be artificially stimulated and activated by prostheticdevices that pass pulses of electrical current through electrodes onsuch a device. The passage of current causes changes in electricalpotentials across visual neuronal membranes, which can initiate visualneuron action potentials, which are the means of information transfer inthe nervous system.

Based on this mechanism, it is possible to input information into thenervous system by coding the information as a sequence of electricalpulses which are relayed to the nervous system via the prostheticdevice. In this way, it is possible to provide artificial sensationsincluding vision.

One typical application of neural tissue stimulation is in therehabilitation of the blind. Some forms of blindness involve selectiveloss of the light sensitive transducers of the retina. Other retinalneurons remain viable, however, and may be activated in the mannerdescribed above by placement of a prosthetic electrode device on theinner (toward the vitreous) retinal surface (epiretinal). This placementmust be mechanically stable, minimize the distance between the deviceelectrodes and the visual neurons, and avoid undue compression of thevisual neurons.

In 1986, Bullara (U.S. Pat. No. 4,573,481) patented an electrodeassembly for surgical implantation on a nerve. The matrix was siliconewith embedded iridium electrodes. The assembly fit around a nerve tostimulate it.

Dawson and Radtke stimulated cat's retina by direct electricalstimulation of the retinal ganglion cell layer. These experimentersplaced nine and then fourteen electrodes upon the inner retinal layer(i.e., primarily the ganglion cell layer) of two cats. Their experimentssuggested that electrical stimulation of the retina with 30 to 100 uAcurrent resulted in visual cortical responses. These experiments werecarried out with needle-shaped electrodes that penetrated the surface ofthe retina (see also U.S. Pat. No. 4,628,933 to Michelson).

The Michelson '933 apparatus includes an array of photosensitive deviceson its surface that are connected to a plurality of electrodespositioned on the opposite surface of the device to stimulate theretina. These electrodes are disposed to form an array similar to a “bedof nails” having conductors which impinge directly on the retina tostimulate the retinal cells. U.S. Pat. No. 4,837,049 to Byers describesspike electrodes for neural stimulation. Each spike electrode piercesneural tissue for better electrical contact. U.S. Pat. No. 5,215,088 toNorman describes an array of spike electrodes for cortical stimulation.Each spike pierces cortical tissue for better electrical contact.

The art of implanting an intraocular prosthetic device to electricallystimulate the retina was advanced with the introduction of retinal tacksin retinal surgery. De Juan, et al. at Duke University Eye Centerinserted retinal tacks into retinas in an effort to reattach retinasthat had detached from the underlying choroid, which is the source ofblood supply for the outer retina and thus the photoreceptors. See,e.g., de Juan, et al., 99 μm. J. Ophthalmol. 272 (1985). These retinaltacks have proved to be biocompatible and remain embedded in the retina,with the choroid/sclera, effectively pinning the retina against thechoroid and the posterior aspects of the globe. Retinal tacks are oneway to attach a retinal array to the retina. U.S. Pat. No. 5,109,844 tode Juan describes a flat electrode array placed against the retina forvisual stimulation. U.S. Pat. No. 5,935,155 to Humayun describes aretinal prosthesis for use with the flat retinal array described in deJuan.

SUMMARY

The present disclosure relates to an apparatus and method for retinalstimulation wherein the apparatus allows for the placement of aprosthetic device on the inner retinal surface to provide artificialsensations including vision; and wherein visual perception threshold isdetermined and stimulation parameters are varied, including frequency,pulse width, and pattern of pulse trains.

According to a first embodiment of the present disclosure, a retinalstimulation method is provided, comprising: generating a stimulationpattern by stimulating a retina of a patient with an impulsiveelectrical signal; and determining how visual perception depends on thegenerated stimulation pattern by observing perceptual threshold as afunction of features of the impulsive electrical signal.

According to a second embodiment of the present disclosure, a method fordetermining visual perceptual threshold is provided, comprising:exposing subjects to a series of variable current stimuli; decreasingamplitude of the variable current stimuli if subject answers correctlyto a current stimulus; increasing amplitude of the current stimuli ifsubject answers incorrectly to the current stimulus; and generating apsychometric function based on answers of the subject, wherein a yes-noparadigm is used, and half of the series of variable current stimulicontained no stimulus.

According to a third embodiment of the present disclosure, a method fordetermining visual perceptual threshold is provided, comprising:exposing subjects to a series of variable current stimuli; decreasingamplitude of the variable current stimuli if subject answers correctlyto a current stimulus; increasing amplitude of the current stimuli ifsubject answers incorrectly to the current stimulus; and generating apsychometric function based on answers of the subject, wherein thevariable current stimuli are varied in a 3 up-1 down staircase pattern.

According to a fourth embodiment of the present disclosure, a retinalstimulation apparatus is provided, comprising: means for generating astimulation pattern by stimulating a retina of a patient with animpulsive electrical signal; and means for determining how visualperception depends on the generated stimulation pattern by observingperceptual threshold as a function of features of the impulsiveelectrical signal.

According to a fifth embodiment of the present disclosure, a visualprosthetic apparatus for retinal stimulation is provided comprising animplantable portion and an external portion, wherein the implantableportion comprises a cable, an RF receiver, an inductive coil and anarray of electrodes, for stimulating visual neurons, and the externalportion comprises a frame, a camera, an external coil and a mountingsystem for the external coil.

According to a sixth embodiment of the present disclosure, a retinalstimulation device is provided, comprising: a stimulation patterngenerator to provide a signal to a retina, wherein the stimulationpattern generator generates an impulsive electrical signal comprising apulse train of biphasic pulses, the pulse train having a delay betweenpulses and a pulse train frequency.

According to a further embodiment of the present disclosure, anapparatus or device for performing any of the method claims of thepresent disclosure, alone or in combination, is disclosed.

Further embodiments are disclosed throughout the specification, drawingsand claims of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a brief schematic view of an implanted visual prosthesis.

FIG. 2 is a prospective view of a visual prosthesis.

FIG. 3 is a top view of the visual prosthesis shown in FIG. 2.

FIG. 4 is a perspective view of the implantable portion of a visualprosthesis.

FIG. 5 is a side view of the implantable portion of a visual prosthesisshowing the fan tail in more detail.

FIG. 6 is a graph showing linear-nonlinear models can predict retinalfiring to light stimuli.

FIG. 7 is a graph showing the effect of pulse duration.

FIG. 8 is a graph showing a method for determining visual perceptualthreshold.

FIG. 9 is a graph showing threshold as a function of pulse width.

FIGS. 10A-10C are graphs showing the varying integration rates ofdifferent cell types.

FIG. 11 is a graph showing summation across pulse pairs.

FIG. 12 is a graph showing threshold for pulse pairs.

FIG. 13 is a graph showing fixed duration pulse trains.

FIG. 14 is a graph showing threshold for fixed duration pulse trains of0.075 ms pulse width.

FIG. 15 is a graph showing threshold for fixed duration pulse trains of0.0975 ms pulse width.

FIGS. 16A, 16B are graphs showing threshold for variable duration pulsetrains.

FIG. 17 is a graph showing the relationship between threshold, frequencyand the number of pulses.

FIG. 18 is a graph showing that the thresholds of pulse trains withfrequency below 50 Hz are independent of pulse number.

FIG. 19 is a graph showing that thresholds for pulse trains withfrequencies above 50 Hz are independent of pulse timing.

FIG. 20 is a schematic of a retinal stimulation device comprising astimulation pattern generator.

FIG. 21A-G is a series of bar charts and response graphs where each rowcontains an example of the pulse train stimulus and data with modelpredictions from the constrained model.

FIG. 22 A-C is a series of bar charts and response graphs forsuprathreshold stimulation where each row contains an example of thepulse train stimulus and data with model predictions from theconstrained model.

FIG. 23 is a flow chart showing the preferred model

FIG. 23A is the flow chart of FIG. 23 in more detail.

FIG. 24 A-C is a series of bar charts and response graphs where each rowshows a novel pulse train stimulus and data with model predictions fromthe constrained model.

FIG. 25 A-C is a series of bar charts and response graphs where each rowshows a novel pulse train stimulus and data for suprathreshold responseswith model predictions from the constrained model.

FIG. 26 A-C are summary charts showing the stimulation responsepredictions resulting from the preferred model.

DETAILED DESCRIPTION

FIG. 1 is a schematic view of a prosthesis for stimulating retinalcells. Patients suffering from retinitis pigmentosa (RP) sustain severevision loss as a result of photoreceptor death. In the preferredprosthesis, the electrode array is aligned in a 4×4 matrix implantedepiretinally, which covers about 10 degrees of visual angle. The uppersub figure shows a schematic of an electrode array in a 4×4configuration. The subfigure from this schematic details a graphicrepresentation of the system of neural cells under each electrode,wherein the neural cells shown are no longer organized, but unorganizedwith significant cell death.

FIGS. 2 and 3 show two different perspective views of a visualprosthesis apparatus according to the present disclosure. The visualapparatus provides an implantable portion 100 and an external portion 5.Portion 5 is shown in FIGS. 2 and 3. Portion 100 is shown in FIGS. 4 and5. The external portion 5 comprises a frame 10 holding a camera 12, anexternal coil 14 and a mounting system 16 for the external coil 14. Themounting system 16 also encloses the RF circuitry.

Three structural features are provided in the visual prosthesis tocontrol the distance, and thereby reduce the distance, between theexternal coil 14 and the inductive (internal) coil (116, FIG. 4). Thethree structural features correspond to movement of the external coilalong the three possible spatial axes occupied by the two coils. Thatis, the external and inductive coils can be viewed as being separated inanatomical axes: the medial-lateral, superior-inferior, and theanterior-posterior axis.

In this way, the first structural feature reduces the distance betweenthe coils along the medial-lateral axis by bending the external coil 14.The distance in this medial-lateral axis should be equivalent to theseparation distance of the coils if the centers of the coils arealigned. The enclosure of the external coil 14 is attached to themounting system 16, which is attached to the leg frame 10 of the visualapparatus. While the RF circuitry within the mounting system 16 is inline with the leg frame, the external coil has been given a preferentialbend 18 towards the face using a flexible connector. With the externalcoil 14 angled toward the face (e.g. at 25 degrees) (see FIGS. 2 and 3),the external coil 14 makes contact with the subject's face and theflexible connector allows conformation to the subject's facial contours.Thus, the external coil 14 is brought in as close as possible in themedial-lateral axis for the subject.

The second structural feature is a sliding bar mechanism controllingmovement along the anterior-posterior axis. The point at which themounting system 16 connects to the visor allows for 7 mm of adjustmentalong this anterior-posterior axis. The sliding bar mechanism can befixed in place when the optimal position is found by tightening twoscrews on the sides of the sliding bar.

The third structural feature is adjustment of the visual apparatus alongthe superior-inferior axis by varying the placement of the visualapparatus along the subject's nose. When the visual apparatus is wornclose to the face, the external coil 14 is higher, and when worn furtherfrom the face, the external coil 14 is lower. Using these threestructural adjustments in combination, the coil separation distance canbe adjusted to obtain an optimal RF link for individual subjects.

FIG. 4 shows a perspective view of an implantable portion 100 of aretinal prosthesi as disclosed. An electrode array 110 is mounted by aretinal tack or similar means to the epiretinal surface. The electrodearray 110 is electrically coupled by a cable 112, which can pierce thesclera and be electrically coupled to an electronics package 114external to the sclera. Electronic package 114 includes the RF receiverand electrode drivers.

The electronics package 114 can be electrically coupled to a secondaryinductive coil 116. In one aspect, the secondary inductive coil 116 ismade from wound wire. Alternatively, the secondary inductive coil may bemade from a thin film polymer sandwich with wire traces depositedbetween layers of thin film polymer. The electronics package 114 andsecondary inductive coil 116 are held together by a molded body 118. Themolded body 118 may also include suture tabs 120. The molded bodynarrows to form a strap 122 which surrounds the sclera and holds themolded body 118, secondary inductive coil 116, and electronics package114 in place. The molded body 118, suture tabs 120 and strap 122 arepreferably an integrated unit made of silicone elastomer. Siliconeelastomer can be formed in a pre-curved shape to match the curvature ofa typical sclera. Furthermore, silicone remains flexible enough toaccommodate implantation and to adapt to variations in the curvature ofan individual sclera. In one aspect, the secondary inductive coil 116and molded body 118 are oval shaped, and in this way, a strap 122 canbetter support the oval shaped coil.

The entire implantable portion 100 is attached to and supported by thesclera of a subject. The eye moves constantly. The eye moves to scan ascene and also has a jitter motion to prevent image stabilization. Eventhough such motion is useless in the blind, it often continues longafter a person has lost their sight. Thus, in one embodiment of thepresent disclosure, the entire implantable portion 100 of the prosthesisis attached to and supported by the sclera of a subject. By placing thedevice under the rectus muscles with the electronics package in an areaof fatty tissue between the rectus muscles, eye motion does not causeany flexing which might fatigue, and eventually damage, the device.

FIG. 5 shows a side view of the implantable portion of the retinalprosthesis, in particular, emphasizing the fan tail 124. When theretinal prosthesis is implanted, it is necessary to pass the strap 122under the eye muscles to surround the sclera. The secondary inductivecoil 116 and molded body 118 must also follow the strap under thelateral rectus muscle on the side of the sclera. The implantable portion100 of the retinal prosthesis is very delicate. It is easy to tear themolded body 118 or break wires in the secondary inductive coil 116. Inorder to allow the molded body 118 to slide smoothly under the lateralrectus muscle, the molded body is shaped in the form of a fan tail 124on the end opposite the electronics package 114. Element 123 shows aretention sleeve, while elements 126 and 128 show holes for surgicalpositioning and a ramp for surgical positioning, respectively.

In order to further understand the effects of retinal stimulation,others have applied sophisticated models for temporal processing oflight stimuli in the in vitro retina. However, there are some cleardistinctions between in vivo studies of implanted subjects and in vitrophysiological research. In the present disclosure, the behavioralresearch will be studied, as opposed to electrophysiology of the invitro retina, and study the behaviors of awake humans as opposed to ananimal model. In addition, a degenerated retina and not a normal,healthy retina will be studied. For example, in RP, retinal degenerationis not simply a loss of photoreceptors. RP patients suffer a loss ofother cell types as well, along with significant reorganization andpossible changes in circuitry and cell function. As one might surmise,the degenerated retinal system is likely to have different temporalproperties than a normal retina.

In the present disclosure, in order to determine how human visualperception depends on the timing of electrical stimulation, a temporalintegration was studied during electrical stimulation. The objectives ofthis include: (1) determination of the potential neurophysiologicalelements underlying visual perception; and (2) development of alinear-nonlinear model of the temporal integration dynamics ofelectrical stimulation. It is of interest to understand temporalintegration properties because it is thought that this information willhelp to generate the most effective stimulation patterns. The first stepis to look at how visual perception depends on the timing of electricalstimulation patterns.

FIG. 6 shows a graph of how linear-nonlinear models can predict retinalfiring to light stimuli. As noted above, there are models in the artthat evaluate the early visual system's response to light stimuli. Oneexample is a model of temporal contrast adaptation in retinal ganglioncells, where the resulting spike train can be predicted based solelyupon the light stimulation input (Chander, D. and E. J. Chichilnisky(2001), Journal of Neuroscience 21(24): 9904-16; Kim, K. J. and F. Rieke(2001), J Neuroscience 21(1): 287-99; Baccus, S. A. and M. Meister(2002), Neuron 36(5): 909-19.)

The linear/nonlinear model aides in the prediction of ganglion cellresponses to light stimuli, wherein a light flicker stimulus isconvolved with a linear filter with a particular time constant. Theoutput of this convolution is then passed through an expandingnonlinearity to ultimately predict the neural response. To evaluatewhether such a model is able to predict the perceptual response toelectrical stimulation, and how the temporal properties differ whenusing electrical stimulation rather than light stimulation, perceptualthreshold is observed as a function of pulse width.

FIG. 7 shows a graph of a biphasic pulse. In accordance with FIG. 7, thestimuli are single, biphasic, cathodic-first, charge-balanced pulses,wherein the pulse width varied between 0.075 milliseconds (ms) and 4 ms,per phase. Anodic pulses are approximately fifty percent as effective ascathodic pulses, thus the anodic pulses are not necessary to consider(Jensen, R. J., O. R. Ziv, et al. (2005), Invest Ophthalmol Vis Sci46(4): 1486-96).

Furthermore, the anodic pulses are considered to be far less effectiveat driving a response in the in vitro retina. This is the result of theorientation of the stimulating electrode relative to the ganglion cell.In this configuration, the negatively-charged cathodic pulse ‘pulls’ thepositive cations within the cell towards the axon hillock, where thereis the highest concentration of voltage-gated channels. Therefore, forthe method according to the present disclosure, the anodic phase shouldnot be considered when it comes to evaluating the biphasic pulse and itsinfluence on perception.

FIG. 8 shows a graph of a method for determining visual perceptualthreshold, wherein the threshold was determined as follows. Subjectswere exposed to a series of stimuli using a yes-no paradigm wherein halfthe trials contained no stimulus. The subjects reported whether thetrial contained a stimulus or not. The current amplitude was variedusing a 3 up, 1 down staircase. In other words, if the subjects got 3correct answers in a row the subsequent current signal was made moredifficult by decreasing the current a step. Likewise, if the subjectanswered incorrectly, the subsequent current signal was made easier byincreasing the current by one step. Thresholds were measured on singleelectrodes using a single interval, yes-no procedure. On each trial,subjects were asked to judge whether or not each trial contained astimulus. This reporting procedure meant that subjects were likely toreport stimulation for either a light or dark spot; subjects wereexplicitly instructed to include either type of percept in making theirdecision. Half of the trials were stimulus-absent catch trials. Duringeach staircase, only amplitude varied. All other parameters (frequency,pulse width, pulse train duration, and the number of pulses) were heldconstant. Each threshold was based on a minimum of 125 trials and errorbars were estimated using Monte-Carlo simulation (Wichmann and Hill,2001).

The curve shown in FIG. 8 is an example of a generated psychometricfunction, which was used to analyze the behavioral data. The x-axis isthe current amplitude and the y-axis is the probability that the subjectsaw the stimulus, 1 being that the subject saw it every time at thatparticular current. The black dots are the subject/patient responses fora specific stimulus condition (a specific current amplitude), with thelarger dots representing a greater number of trials at that condition.As is shown in FIG. 8, there is a dramatic shift in performance between10 uA and 16 uA. After adjusting the curve to the false alarm rate, thecurve was fit with a Weibull function and the 50% point was thedetermined threshold. The Weibull function allows for many differentdistributions. This function is a common cumulative distribution that isfrequently used for life data because its slope parameter can beadjusted to allow the curve to represent different distributions.

FIG. 9 is graph showing threshold as a function of pulse duration orwidth. FIG. 9 is an example curve (typical of data from 10 electrodes, 2subjects). Data can be modeled using a simple leaky integrator model. Aleaky integrator model represents the accumulation and dissipation ofsome input (e.g. electric current or charge) that accumulates anddissipates with a specific rate that depends on the value of the timeconstant. Across all data in FIG. 9, time constants of <1 ms are found,which is consistent with chronaxie values for ganglion cell integrationperiods (Jensen et al., 2005). The pulse width is on the x-axis varyingbetween 0.075 ms and 4 ms, and the y-axis is the amplitude to reachthreshold. The eight boxes shown in the figure represent measuredthresholds at their corresponding pulse widths. So, for example, at0.075 ms, it requires approximately 425 microAmperes (μA) of current forthe patient to be able to see that stimulus 79% of the time. The datashow that as the pulse width is increased, there is a decrease incurrent amplitude needed to reach the threshold. The black line,represents the current model and the fit estimation of this particulardata set. Additionally, this data can be fit using a simple leakyintegrator model (Kandel, E. R., J. H. Schwartz, et al. (1991).Principles of Neural Science. Norwalk, Conn., Appleton & Lange) having asingle free parameter (tau or time constant) that represents theintegrative behavior of the system.

FIGS. 10A-10C show that different cell types integrate charge atdifferent rates with cathodic phases in grey and anodic phases in black.FIG. 10 also shows how a leaky integrator model would integrate abiphasic pulse (FIG. 10A) using a short (FIG. 10B) and long (FIG. 10C)time constant. FIG. 10A represents an input stimulation pattern(biphasic pulse). FIG. 10B represents a fast integrator response to theinput, typical of ganglion cells. FIG. 10C represents a slow integratorresponse, typical of bipolar cells.

For further example, one can imagine two different biphasic pulses thatdiffer in their pulse width, where one is relatively long and the otheris short. If a leaky integrator model is applied with fast temporalproperties, the response curve follows the shape of the input reasonablywell. On the other hand, if the model integrates more slowly, theresponse is more sluggish, as represented in FIG. 10C by the shallowerslope of the response curve. In fact, if the biphasic pulse is short,the amplitude of the response curve is greatly diminished. Applying thisconcept to the physiology of Jensen (Jensen et al., 2005) and Fried(Fried, S. I., H. A. Hsueh, et al. (2006), J Neurophysiol 95(2): 970-8.)who reported that integration periods of ganglion cells aresubstantially faster than those of either bipolar or amacrine cells,suggests that it may be possible to exclusively activate ganglion cellswith shorter pulse widths.

Another approach to evaluating the temporal integration of the system isby looking at how two separate pulses sum in time. FIG. 11 is a graphshowing summation across pulse pairs. Stimuli were 0.075 mspseudo-monophasic cathodic pulses. The first pulse had fixed currentamplitude (sub-threshold). The second pulse followed with a variabledelay (0.15-12 ms). The experiment, illustrated by FIG. 11, evaluatesthe summation across pulse pairs. In other words, the experimentdetermines how the first pulse, (i.e. the conditioning pulse)contributes to the threshold response of the second pulse, (i.e. thetest pulse). The stimuli were pseudo-monophasic because, for obvioussafety reasons, a charge-balanced anodic phase is included, as shown bythe positive pulse to the right of FIG. 11. The difference here is thatthe anodic pulses were presented later in time by about 30 ms.

FIG. 12 is a graph showing threshold for pulse pairs. The graph derivesfrom a data set of 8 different electrodes across two subjects. The timeconstants were the same (<1 ms) as the single pulse data are consistentwith ganglion cell stimulation. With pulse pair summation it wasdetermined that there is a critical window of integration.

In particular, the x-axis of FIG. 12 shows the delay between pulsepairs, and the y-axis is the amplitude to reach threshold. The criticalwindow of integration was observed to be somewhere short of onemillisecond. More specifically, looking at the portion of the curvebefore the 1 ms delay value, a short increase in delay provides a largeincrease in amplitude to reach threshold. On the other hand, after theone millisecond point, the curve asymptotes and the current value atwhich it asymptotes is the same as that for a single biphasic pulse.This observation means the following: first, that the secondary anodicphase has no influence on threshold, and secondly, that the integrationperiod is very short. If these data were fitted to a leaky integratormodel, time constants would be similar to those of ganglion cells.

Therefore, all the data shown thus far provide a strong indication ofhow simple and very short stimuli are integrated over time. However, afurther objective of the present disclosure is to determine continuousstimulation in order to provide visual information to improve navigationand visual recognition. In view of this further objective, one or twoelectrical pulses are not enough.

FIG. 13 is a graph showing a fixed duration pulse train, i.e. a seriesof multiple pulses where every pulse has the same width. In particular,in order to determine how multiple pulses integrate over time, stimuliwere fixed duration pulse trains of 200 milliseconds. Pulses were either0.975 or 0.075 milliseconds in duration, and frequency varied between 5Hz and 225 Hz. Amplitude of all pulses in the train variedsimultaneously to find threshold. In other words, the amplitude of eachpulse within the pulse train increased and/or decreased at the sametime.

FIGS. 14 and 15 show graphs indicative of threshold for fixed durationpulse trains like the one shown in FIG. 9.

It has already been discussed above that the reduction in the amount ofcurrent needed to reach the threshold is due to interactions betweenpulses. FIG. 14 and FIG. 15 show that the decrease in threshold isdriven by the frequency of the pulses.

The graph of FIG. 14 refers to data coming from pulse trains havingwidths (duration of each pulse) of 0.075 ms. On the other hand, thegraph of FIG. 11 refers to data coming from pulse trains having widthsof 0.975 ms. In both cases, the x-axis frequency range is the same, i.e.5 Hz to 225 Hz. However, there is a significant difference between theamplitude values to reach threshold of the two Figures. The values ofFIG. 14 (between about 300 and about 100 microAmperes) are an order ofmagnitude greater than the values of FIG. 15 (between about 40 and about20 microAmperes). In both graphs, solid lines have been added to showthe behavior of the model.

The reason for the different result is the difference in pulse width(0.075 ms vs. 0.975 ms). In particular, as the pulse width is increased,less current is required to drive the system to threshold, as alsopreviously discussed.

Therefore, it appears that a decrease in threshold is a function offrequency of the pulses. However, the response to pulse trains isdynamic, and the resulting pulse train data cannot be fitted to a leakyintegrator model, as there are interactions between pulses that gobeyond that of the model. Also, there is one potential confound with thepulse train data, and that is that since fixed duration pulse trains arebeing used, in order to change the frequency an increase in the numberof pulses is required. For example, at 15 Hz, 3 pulses are used, and at225 Hz, 45 pulses are used.

In order to determine if a decrease in threshold is a function offrequency or a function of the number of pulses, or a function of both,the applicants have examined the relationship between frequency and thenumber of pulses.

FIGS. 16A and 16B are graphs showing threshold values for variableduration pulse trains. In this example, the stimuli consisted of pulsetrains of 2, 3, and 15 pulses (where the 2 and 3 pulses examples areshown in FIG. 12). The frequency of these pulse trains was varied bychanging the delay between the biphasic pulses. The delay varied from0.075 ms to 300 ms, corresponding to a range of frequencies betweenapproximately 3000 and approximately 3 Hz. As with the fixed durationpulse train data, perceptual threshold was measured by varying theamplitude of all the pulses within the pulse train simultaneously. Inother words, the amplitude of each pulse within the pulse trainincreased and/or decreased at the same time.

FIG. 17 is a frequency vs. amplitude-to-reach-threshold graph similar tothe ones shown in FIGS. 10 and 11, where relationship between frequencyand number of pulses is also shown. Here, the x-axis is represented in alogarithmic scale. Three curves are shown. The curve on top correspondsto a 2 pulse train. The curve in the middle corresponds to a 3 pulsetrain. The curve on the bottom corresponds to a 15 pulse train.Differences in behavior between the different numbered pulse trains donot appear until frequencies above about 20 Hz (about 50 Hz), wherein asthe number of pulses is increased, there is a decrease in necessarycurrent to reach threshold The three curves are separated by 300 ms atthe lowest frequency (3 Hz) and by 0.075 ms at the highest frequency(3333 Hz). It should be noted that these curves, as with all the datapresented, are generated using a Monte Carlo simulation.

The data of FIG. 17 show that there is no statistical difference inperceptual threshold for all three of the different numbered pulsetrains. That is, presenting two pulses at 20 Hz or presenting fifteenpulses at 20 Hz results in the same perceptual threshold, and therefore,perceptual threshold becomes independent on pulse timing. This is moreclearly represented when the data in the fifteen pulse trains isaveraged over six electrodes for two patients. Looking at the higherfrequencies, there is no statistical change in threshold as a functionof frequency, representing independence on timing but a dependence onpulse number. The lower frequencies, as noted above, are independent ofpulse number, but have a clear relationship to pulse timing.

FIG. 18 is a graph showing that thresholds for pulse trains withfrequencies below about 50 Hz are independent of the number of pulses.The graph refers to data for thresholds for the two (grey bar), three(diagonal-lined bar) and fifteen (horizontal-lined bar) pulse train dataof FIG. 17, averaged over six electrodes and over two subjects, plottedfor frequencies of 3, 7, 10 and 20 Hz, wherein the error bars representthe standard error. Although there may be slight statistical differencesbetween these data, and there is a trend downward as a function offrequency for the fifteen pulse data, the statistical differencesbetween the two, three, and fifteen pulse data, when compared at eachfrequency, are very similar. This similarity between pulse trainssuggests that perceptual thresholds of the input are independent ofpulse number. However, for the fifteen pulse data, a dependency on pulsetiming occurs at lower frequencies.

In view of the data in FIG. 19, and the disclosure that ganglion cellsoperate in a range that is somewhere below 250 Hz (O'Brien, B. J., T.Isayama, et al. (2002), Journal of Physiology 538(Pt 3): 787-802), it isdetermined that increasing frequencies above this operating ceiling doesnot supply the system with any additional information about the stimulusbecause ganglion cells are computationally incapable of processingfrequencies in this higher range. In another aspect, if the cortex isthought of as a low pass filter, all the pulses within these higherfrequency trains fall within the limits of this integrative window.Thus, if the window of integration of the cortex is on the order ofseveral hundred milliseconds, as long as all the pulses within thattrain fall within that window (above ˜50 Hz), the response will be thesame.

FIG. 20 shows a stimulation pattern generator 310 which can provide theimpulsive electrical signals to implement a determined stimulationpattern from observing a perceived threshold. This stimulation patterngenerator can be programmed to provide a pattern of pulse trains havinga pulse train frequency and a pulse width. For example, the stimulationpattern generator can be programmed to provide a pulse train having afrequency less than 50 Hz, wherein the pulse width is fixed at 0.075 msor 0.975 ms. Alternatively the stimulation pattern generator can providea pulse train having a frequency higher than 50 Hz, wherein the pulsewidth is variable. As shown, the stimulation pattern generator isconnected to a retinal stimulating device 300. An example of a retinalstimulating device is shown in FIGS. 1 and 2.

Suprathreshold brightness-matching was carried out on single electrodesusing a two-interval, forced-choice procedure. Each trial contained twointervals with each interval containing a pulse train of a differentfrequency. For example, interval 1 might contain a 15 Hz pulse train andinterval 2 might contain a 45 Hz pulse train. Subjects were asked toreport which interval contained the brighter stimulus. A one-up,one-down staircase method was used to adjust the amplitude of the higherfrequency pulse train based on the observer's response. The firstbrightness match was made by fixing the amplitude of a “standard” 5 Hzpulse train (a single pulse within a 200 ms window) to be 2 or 3 timesthreshold amplitude, and finding the amplitude needed for a 15 Hz “test”pulse train to match the brightness of the standard pulse train. The 15Hz pulse train then became the “standard” pulse train and was comparedin brightness to a 45 Hz “test” pulse train and so on. Each brightnessmatch was based on a minimum of 80 trials and error bars were againestimated using an adaptive sampling Monte-Carlo simulation (Wichmannand Hill, 2001). Using this method, we were able to obtain anisobrightness curve that represented the current amplitude needed tomaintain the same subjective brightness across a wide range offrequencies.

In each of our two subjects, we measured detection thresholds for 10different categories of stimulation pattern (FIGS. 21A-G, 24A-C) andsuprathreshold perceived brightness for 6 different categories ofstimulation pattern (FIG. 22A-C, 25A-C). Data were collected from 12electrodes across the two subjects. Across these 12 electrodes, wecollected 534 threshold and 116 suprathreshold measurements in total.Patients typically reported that phosphenes appeared white or yellow incolor, and round or oval in shape. At suprathreshold, percepts werereported as brighter and the shape occasionally became more complex thana simple round or oval shape. The shapes were reported as beingapproximately 0.5-2 inches in diameter at arm's length, corresponding toroughly 1-3 degrees of visual angle. Occasionally, a dark spot ratherthan a white or yellow percept was reported. In this case, the patientwould use the relative contrast of the spot for detection (threshold) or‘brightness comparison’ (suprathreshold).

Data were modeled using a linear-nonlinear model (FIG. 23) similar tomodels of auditory stimulation in cochlear implant users (Shannon,1989), retinal ganglion cell spiking behavior during temporal contrastadaptation (Chander and Chichilnisky, 2001; Rieke, 2001; Baccus andMeister, 2002), and models of human psychophysical temporal sensitivity(Watson, 1986). Here we simply present the components of the model; amore detailed explanation of each stage of the model is described below.We began by convolving the stimulus with a temporal low-pass filter, or“leaky integrator” using a 1-stage gamma function as its impulseresponse:r ₁(t)=f(t)*δ(t,1,τ₁)  (1)where f(t) is the electrical stimulation input pattern, t is time (ms),and δ is the impulse response function with time constant τ₁. (We reporthere time constants (τ) rather than chronaxie values (c), which are alsocommonly reported in the literature: τ=c/ln(2)). The gamma function usedto model the impulse response can be generally described as:

$\begin{matrix}{{{\delta( {t,n,\tau} )} = {\frac{{\mathbb{e}}^{{- t}/\tau_{1}}}{{\tau( {n - 1} )}!}( {t/\tau} )^{n - 1}}},} & (2)\end{matrix}$where t=time, n=the number of identical, cascading stages, and τ is thetime constant of the filter (the 1-stage gamma function in Eq. 1 issimply an exponential function.)

We assumed that the system became less sensitive as a function ofaccumulated charge. This was computationally implemented by calculatingthe amount of accumulated cathodic charge at each point of time in thestimulus, c(t), and convolving this accumulation with a second 1-stagegamma function having a time constant τ₂. The output of this convolutionwas scaled by a factor ε, and then subtracted from r₁ (Eq. 1),r ₂(t)=r ₁(t)−ε(c(t)*δ(t,1,τ₂)).  (3)r₂ was then passed through an expansive nonlinearity,r ₃(t)=(r ₂(t))^(β)  (4)and convolved with a low-pass filter described as a 3-stage gammafunction with time constant τ₃,r ₄(t)=r ₃*δ(t,3,τ₃).  (5)We assumed that the response reached threshold (or the point ofequibrightness during suprathreshold experiments) when

$\begin{matrix}{{\max\limits_{t}( r_{4} )}>=\theta} & (6)\end{matrix}$where θ is a fixed constant.

Optimization was carried out using a subset of the full set of data—2electrodes for each of the two patients (S05-B3 & C2, S06-B1 & C2).

The parameter values τ₁, τ₂ and τ₃ were optimized across the 7 thresholdand 3 suprathreshold experiments using a standard least-squared errorminimization technique. The parameters ε (linear shift as a function ofcharge) and β (power nonlinearity) were fit separately for threshold andsuprathreshold levels of stimulation. When fitting suprathreshold data,ε and β were allowed to vary across different levels of apparentbrightness.

The parameter that represented the model output at threshold, θ, wasallowed to vary across each experiment on a given electrode. Variationin θ accounts for differences in mean sensitivity between the twopatients, differences in sensitivity across electrodes, and slightchanges in electrode sensitivity over time. The set of data in thispaper were collected over slightly more than a two year period, duringwhich we observed gradual changes in sensitivity over time whichappeared to be mainly due to slight changes in the position of theelectrode array over time. Because each experiment on a given electrodewas collected over a relatively short time period (usually within a weekor two) we assumed that electrode sensitivity did not vary within anexperiment.

After optimizing the model using a subset of the full set of data, weaveraged the best-fitting parameters values for τ₁, τ₂, τ₃, ε and βacross all the four electrodes used for optimization and used these meanvalues to predict threshold and suprathreshold data for novelelectrodes. For these novel electrodes the only parameter allowed tovary across each experiment was the threshold parameter, θ.

The solid lines in FIGS. 21A-G show model predictions to threshold datafor a single novel electrode for each of the two patients (S05-C3,S06-A1). The solid curves in FIGS. 22A-C show suprathreshold modelpredictions for a single novel electrode for each of the two patients(S05-C4, S06-B2). The model and parameter values generalized tosuccessfully predict data on novel electrodes.

We then examined the ability of the model to predict responses to novelpulse train waveforms not used to optimize model parameters. We againused fixed values for τ₁, τ₂, τ₃, ε and β based on the electrodes andstimulus patterns used for optimization, and the only parameter allowedto vary across each experiment was the threshold parameter, θ.

The novel waveforms consisted of repeated bursts of 3 pulses with avariable inter-burst delay. Data for this novel waveform was collectedat both threshold and suprathreshold levels of stimulation on novelelectrodes not used for the original model fits (S05-A1, S06-A2).Results are shown in FIGS. 24 and 25, respectively. The model andparameter values generalized to successfully predict these data from anovel stimulation pattern on a novel electrode.

Our model, like those describing the perception of light stimuli,presumably approximates the responses of neuronal populations. In thecase of our threshold experiments, it is possible that firing within arelatively small number of retinal cells mediated detection. Electricalstimulation thresholds for single pulses (FIG. 21A) are comparable tothose reported in the animal in vitro electrophysiological literature.This is surprising, given that the definition of threshold routinelywithin these in vitro studies is the current that reliably elicits atleast one spike in a single cell. However it has been previously shownthat subjects with normal vision can reliably detect a single photon oflight (Hecht et al., 1942), suggesting that a very small increase overthe baseline firing rate of ganglion cells is probably sufficient tomediate behavioral detection. Thus, thresholds in our subjects may havebeen mediated by a relatively small number of spikes: these spikesmight, of course occur either in a single cell or across several cells.At suprathreshold our model presumably approximates the populationresponse of a larger number of cells each producing one or multiplespikes.

We now provide detailed description of each component and parameter ofthe model.

τ₁ (Eq. 1). The parameter τ₁ represents the time course of the firststage of current integration. The value was mainly constrained by theshape of the functions describing how threshold amplitude decreases as afunction of pulse duration for single pulses (FIG. 21A) and howthreshold increases as a function of pulse pair separation (FIG. 21B).Estimates of τ₁ in our model varied between 0.24-0.65 ms, with a mean of0.42 ms, a value very similar to electrophysiology estimates of theintegration of current by ganglion cells. Extracellular electricalstimulation of retinal ganglion soma results in measured time constantsthat vary between 0.22 ms and 0.51 ms (Jensen et al., 2005a; Fried etal., 2006; Sekimjak et al., 2006). It should be noted that intracellularcurrent injection seems to result in much slower time constants (O'Brienet al., 2002), that were greater than 3.9 ms. One possibility is thatthe time constant of extracellular stimulation is based on theactivation of the sodium channel current in ganglion cells, which is onthe order of 0.1 ms, rather than upon the time constant of the entiremembrane (Litpon, 1987). In contrast, the time constants of bipolar andamacrine cells are estimated to be far slower. It is thought that thelong-latency spiking in ganglion cells, occurring >8-60 ms after thebeginning of electrical stimulation (Greenberg, 1998; Jensen et al.,2005a; Fried et al., 2006), probably originates from bipolar cells sincea cocktail of synaptic blockers completely suppresses this late-phasespiking in ganglion cells. The measured time constant associated withthese longer latency spikes varies between 20-26 ms, depending onelectrode size. The time constant associated with the inhibitory inputfrom amacrine cells is on the order of 100-200 ms (Fried et al., 2006).The similarity of τ₁ to time constants of current integration byganglion cells suggests that direct stimulation of ganglion cells(rather than indirect stimulation via pre-synaptic input) may beprimarily responsible for integration of stimulation current within theretina. ε and τ₂ (Eq. 3) The parameters ε and τ₂ representdesensitization as a consequence of accumulated charge, where εrepresents the strength of desensitization and τ₂ represents the timeconstant over which charge was integrated. The values ε and τ₂ weremainly determined by the difference in the data curve slopes between the0.075 and 0.975 ms pulse trains as a function of frequency for boththreshold and suprathreshold data (FIGS. 21C & D, FIG. 22). As frequencyincreases there is a decrease in the amount of current needed, perpulse, to reach threshold. However, the slope of this decrease wassteeper for 0.075 than for 0.975 ms pulses, consistent withdesensitization as a function of accumulated charge. ε ranged from 2 to3 with a mean of 2.25 for threshold stimulation, and between 8 to 10with a mean of 8.73 for suprathreshold stimulation. Estimates of τ₂ranged between 38 and 57 ms with a mean of 45.25 ms.

There are two possible sources for this change in sensitivity as afunction of previous charge. One possibility is that injected chargedirectly results in a hyperpolarization of membrane resting potentialswithin individual ganglion cells. Shifts in resting potentials that seemto be analogous to slow contrast adaptation effects, can be produced inganglion cells by injection of hyperpolarizing current (Baccus andMeister, 2002). However it is also likely that inhibition frompresynaptic cells plays a role in the desensitization we observed.Inhibitory presynaptic influences on spiking in response to electricalstimulation have been described by Fried et al. (Fried et al., 2006),especially for longer pulses. It seems likely that the desensitizationstage of our model simply approximates a series of complex adaptiveprocesses, with time courses varying between milliseconds to tens ofseconds (Chander and Chichilnisky, 2001; Rieke, 2001; Baccus andMeister, 2002), occurring both in the retina and beyond. β (Eq. 4). Theparameters β describes an expanding input-output nonlinearity. Powernonlinearities have been proposed in a variety of linear-nonlinearmodels developed to describe spiking as a function of contrast in singleganglion cells (Chander and Chichilnisky, 2001; Baccus and Meister,2002). A similar nonlinearity has also been used to model humanbehavioral data describing the perceptual temporal integration of lightstimuli (Watson, 1986). In the case of our model and that of Watson,this power function presumably describes the input-output nonlinearityacross a population of cells. β was constrained by the slopes describingthe decrease in the amount of current required to reach threshold or agiven level of brightness with increasing frequency (FIG. 21C-G, FIG.22). β varied between 3.0-4.2, with a mean of 3.43 for thresholdstimulation. Lower values of β were required to fit suprathreshold data.Depending on the brightness level, values of β ranged between 0.6-1.0,with a mean of 0.83. An increase in the brightness of the percept to bematched led to a decrease in the slope of the response nonlinearity. Onepossibility is that as the intensity of stimulation increases, neuronswith shallower input-output nonlinearities are recruited. Alternatively,this change in the power function may be driven by changes in theinput-output nonlinearity within individual cells. It has been found inmodels of retinal spiking that the slope of the nonlinearity changes asa function of increased contrast (Rieke, 2001; Baccus and Meister,2002). τ₃ (Eq. 5) The parameter τ₃ determines the integration period ofthe final low pass filter. This time constant was primarily determinedby the shapes of the curves of (FIG. 21E-G). Thresholds decrease as afunction of frequency for a fixed number of pulses, with an asymptote ataround 100-200 Hz, with the effect being most noticeable for the pulsetrain containing 15 pulses. (At frequencies above 1000 Hz there was aslight increase in threshold, in our model which was due to the firstintegration time constant, τ₁.) τ₃ was found to range between 24-33 ms,with a mean of 26.25 ms. It is possible that τ₃ may represent the slowtemporal integration that occurs in cortex: similar integration timeshave been found in simple cell recordings in cat striate cortex (Reid etal., 1992), and Watson's model of a wide range of psychophysical dataexamining the integration of temporal light stimuli requires ananalogous second-stage low-pass filter with a roughly similar timeconstant (Watson, 1986).

The power of this model was significantly higher than that of a lessconstrained model where τ₁, τ₂, τ₃, ε and β were all allowed to varyacross each experiment and electrode (F test, F_(ratio)=0.2501, α<0.01).While there were some small deviations between the model and the data,these deviations were relatively small compared to comparable models ofpsychophysical performance for temporal light stimuli e.g. (Watson,1986; Foley and Boynton, 1994). There were some systematic deviationsbetween the model and performance for long pulses at suprathresholdlevels of stimulation (FIGS. 22 B&C). It is perhaps not surprising thatour model did not generalize completely to suprathreshold levels ofstimulation with long pulses given that neurophysiological data suggeststhat presynaptic cells will have a much larger influence on neuronalresponses to such stimuli (Fried et al., 2006).

This model is also highly constrained compared to analogous models thathave been used to model human responses to temporally varying lightpatterns e.g. (Watson, 1986; Foley, 1994). In these psychophysicalmodels a similar number of parameters are required, a smaller range oftemporal patterns are generally modeled, and parameters are typicallyallowed to vary across subjects. This model is also constrained relativeto a similar model of temporal sensitivity in cochlear implants(Shannon, 1989) where once again, a similar number of parameters wasrequired, a smaller range of temporal patterns was modeled, andparameters were allowed to vary across subjects. Finally, this model isconstrained compared to similar models that have been used to describethe spike timing response of retinal ganglion cells (Chander andChichilnisky, 2001; Rieke, 2001; Baccus and Meister, 2002). In thesemodels a similar number of parameters are required to describe cellresponses, a smaller range of temporal patterns are modeled, andparameters of the model are allowed to vary across each individual cell.

Achieving useful percepts requires satisfying a variety of safety andengineering constraints. First, we assume that useful percepts requirestimulation at frequencies higher than subjects' perception of visibleflicker (frequencies above the “critical flicker frequency”). Second,safety concerns dictate relatively stringent charge density limits,since high charge densities have the potential to compromise theintegrity of electrode material (Brummer and Turner, 1975; Brummer etal., 1983) and cause damage to stimulated neural cells (McCreery et al.,1988; McCreery et al., 1990; Shannon, 1992). Third, the maximum currentamplitude that can be produced may in some cases be limited by thecompliance voltage of the stimulator. A final set of constraints includelimits in the amount of power available to the implant given the needfor a long battery life, and power limits inherent in transmitting powerinductively, resulting in a need to minimize overall charge.

Our model allows us to determine the optimal stimulation pattern neededto produce a percept of a given brightness level given theseconstraints. FIG. 26 shows example predictions of threshold currentamplitude (FIG. 26A), charge density (FIG. 26B), and overall charge(FIG. 26C) for a 500 ms pulse train presented on an electrode of typicalsensitivity across a range of pulse widths and frequencies. The dashedlines represent examples of safety and engineering constraints thatmight restrict the potential set of stimulation patterns. We assumedthat stimulation must be at a rate higher than a critical flickerfrequency of 50 Hz (Graham, 1965), a current amplitude limit of 200μAmps, and a charge density limit of 0.35mC/cm². Given these exampleconstraints, our model predicts that the most charge efficientstimulation pattern is a 50 Hz pulse train consisting of 0.089 mspulses. Of course this ability to evaluate engineering and safetytrade-offs across different pulse patterns need not be restricted tosimple stimulation patterns such as those used in this example.

We report here the first quantitative model of the perceptual effects ofelectrical retinal stimulation in retinitis pigmentosa patients. Visualperceptual responses could be predicted with a surprisingly simple modelthat bears a close resemblance to models of ganglion cell firingbehavior during contrast adaptation (Chander and Chichilnisky, 2001;Rieke, 2001; Baccus and Meister, 2002), human temporal integration oflight stimuli (Watson, 1986), and auditory processing in cochlearimplant users (Shannon, 1989).

Models such as ours may provide some insight into the neural pathwaysresponsible for responding to electrical stimulation. The integrationtime course of the first stage (τ₁) of our model supportselectrophysiology data (Jensen et al., 2005b, a) suggesting that directstimulation of ganglion cells may be the primary source of percepts inepiretinal electrical stimulation. The need to include desensitizationas a function of charge in our model suggests that processes similar tothose found in contrast gain control for light stimuli (Chander andChichilnisky, 2001; Rieke, 2001; Baccus and Meister, 2002) may alsooccur during electrical stimulation, consistent with electrophysiologydata on the effects of injecting hyperpolarizing current from Baccus andMeister (Baccus and Meister, 2002). Finally, the time constant of thefinal stage of our model is consistent with the slow integration timeperiods found within cortex (Watson, 1986; Reid et al., 1992),suggesting that this stage of our model may represent cortical ratherthan retinal processes.

A successful retinal prosthesis will need to produce percepts consistingof regions of constant brightness and across a range of brightnesslevels, while satisfying a complex set of engineering constraints:charge densities must remain relatively low, it is technically difficultto produce very high current amplitudes, and absolute charge must beminimized to maximize battery life. Models of the perceptual effects ofelectrical stimulation, such as that described here, will be critical inallowing electrical stimulation protocols to be selected that bestsatisfy these many constraints.

Of course, a wide variety of challenges remain. For example, apparentbrightness is not the only perceptual quality that needs to beconsidered. It is possible that different temporal patterns stimulateslightly different subpopulations of neurons, resulting in distinctpercepts. Moreover, our experiments only considered pulse trains ofrelatively short duration (a maximum of a few seconds). Longer periodsof continuous stimulation (minutes or hours) may result in long-termadaptation, sensitization, and/or retinal rewiring. It is quite likelythat frequent electrical stimulation over a time scale of weeks andmonths may result in changes in retinal connectivity and responsivity(Marc et al., 2003). Additionally, it is of course of criticalimportance to understand how neighboring electrodes may interact in thespatiotemporal domain. Our model simply predicts sensitivity over timeat the single electrode level, the extension of models such as ours tothe spatial domain is an obvious next step.

Finally, a successful prosthesis will involve designing arrays which arestable on the retina, map to predictable locations in space, and are ofhigh enough resolution to provide the quality of visual informationneeded to perform useful real world tasks.

Referring to FIG. 21 Each row contains an example of the pulse trainstimulus (Column 1) and data (gray symbols) with model predictions fromthe constrained model (solid lines, see below) for patients S05 (Column2) and S06 (Column 3). All plots are log-linear. Error bars generatedusing a Monte-Carlo simulation are shown (some error bars are smallerthan the data symbol). These data are from electrodes C3 and A1, frompatient S05 and S06, respectively. (A) Single Pulse Threshold. Stimuliwere single, biphasic, charge-balanced square pulses, whose pulse widthvaried in duration from 0.075 ms to 4 ms (dotted arrow). Anodic andcathodic phases had equal duration and amplitude. For each pulse width,the amplitude was varied (solid arrow) to determine perceptualthreshold. In the data plots, the x-axis represents pulse width and they-axis represents the current needed to reach threshold. As pulse widthincreases there is an exponential decrease in the current amplitudeneeded to reach perceptual threshold. (B) Exp 2. Latent Addition.Stimuli were 0.075 ms pseudo-monophasic pulse pairs (the anodic phaseswere presented 20 ms after the end of the second cathodic pulse). Theinitial “conditioning” cathodic pulse always had fixed amplitude (50% ofthe single pulse threshold). The delay between the start of theconditioning pulse and the start of the test pulse varied between 0.15ms and 12 ms (dotted arrow). After this variable delay, a secondcathodic “test” pulse was presented. The amplitude of this test pulsewas varied to determine threshold (solid arrow). In each data plot, thex-axis represents the delay between the conditioning and the test pulse.As the delay between the two pulses increases, the current necessary forthe second pulse to reach threshold increases. (C & D) Short Pulse andLong Pulse Fixed Duration Pulse Train. Stimuli were 200 ms pulse trainswhose frequency varied between 5 Hz and 225 Hz. In the short pulse fixedduration pulse train experiment the pulse width was 0.075 ms and in thelong pulse fixed duration pulse train the pulse width was 0.975 ms. Theamplitude of all pulses within the train was varied to determinethreshold. In these data plots, the x-axis represents frequency and they-axis represents the current amplitude (across all pulses) needed toreach threshold. As frequency increases there is a roughly exponentialdecrease in the necessary current to obtain threshold. (E, F & G)Variable Duration Pulse Train with 2, 3 or 15 Pulses. Stimuli were pulsetrains whose frequency was varied between 3 Hz and 3333 Hz. Pulse trainscontained 2, 3 or 15 pulses. The amplitude of all pulses within thetrain was varied simultaneously to determine threshold. In these data,the x-axis represents frequency and the y-axis represents the currentamplitude (across all pulses) needed to reach threshold. As frequencyincreases, there is a decrease in necessary current to reach threshold.At extremely high frequencies there is a slight increase in threshold.

Referring to FIG. 22. (A) Suprathreshold—Short Pulse (2 timesthreshold). Stimuli were 200 ms pulse trains consisting of 0.075 mspulses, whose frequency varied between 5 Hz and 135 Hz. The amplitudevalue for the 5 Hz train was set at 2 times threshold and the amplitudeof the 15 Hz pulse train was modulated to find the amplitude that wasequally bright to that of the 5 Hz pulse train. We then obtained anisobrightness curve for frequencies from 5 Hz to 135 Hz, as described inthe main text. The black line represents the prediction of our model. Ingeneral, there is a decrease in necessary current per pulse to reachequibrightness as frequency increases. (B) Suprathreshold—Long Pulse (2times threshold). Stimuli were 200 ms pulse trains consisting of 0.975ms pulses, whose frequency was varied between 5 Hz and 135 Hz. Again,there is a decrease in necessary current per pulse as frequency isincreased. (C) Suprathreshold—Long Pulse (3 times threshold). Here theamplitude of the 5 Hz train was set to 3 times the threshold value.Again, there is a decrease in necessary current per pulse as frequencyis increased. Data for 3 times threshold was not collected for shortpulse trains because this would have required stimulating above safetylimits.

FIG. 23 is a schematic of the model. The signal input is convolved witha 1-stage linear filter (Eq. 1). The signal is then passed through ashifting, power nonlinearity (Eqs. 3 & 4), where the shift depends onthe amount of previously presented charge within the pulse train and theslope of the nonlinearity depends on the extent to which the stimulus usabove threshold (see below). The output of the nonlinearity is thenconvolved with a 3-stage linear filter with a much longer time constant(Eq. 5). Finally, we assumed that a stimulus was at visual threshold (ora given brightness level) when its final response reached a thresholdvalue (Eq. 6).

Referring to FIG. 24, each row contains an example of the novel pulsetrain stimulus (Column 1) and threshold data with model predictions forpatients S05 (Column 2) and S06 (Column 3). All pulse trains consistedof a 500 ms pulse train consisting of bursts of three pulses. Each burstconsisted of 0.45 ms biphasic pulses with no inter-phase delay. Thex-axis represents the delay between each set of 3 bursting pulses. A)Threshold Bursting—15 Pulse. Stimuli consisted of 5 bursts. The interpulse delay between each of the three pulses in each burst variedbetween 0.075-32.4 ms. For the 32.4 ms inter pulse delay the pulses wereevenly distributed throughout the 500 ms time period of stimulation.This inter pulse delay is represented on the x-axis. The y-axis is thecurrent needed to reach perceptual threshold. (B) Threshold Bursting—30Pulse. Stimuli consisted of 10 bursts. The inter pulse delay betweeneach of the three pulses in each burst varied between 0.075-15.75 ms,with the pulses evenly distributed throughout the 500 ms time period ofstimulation for the 15.75 ms inter pulse delay. (C) ThresholdBursting—60 Pulse. Stimuli consisted of 20 bursts. The inter pulse delaybetween each of the three pulses in each burst varied between0.075-7.425 ms, with the pulses evenly distributed throughout the 500 mstime period of stimulation for the 7.425 ms inter pulse delay.

Referring to FIG. 25, each row contains an example of the pulse trainstimulus (Column 1) and suprathreshold data with model predictions forpatients S05 (Column 2) and S06 (Column 3). All pulse trains consistedof a 500 ms pulse train consisting of bursts of three pulses. Each burstconsisted of 0.45 ms biphasic pulses with no inter-phase delay. Thex-axis represents the inter-pulse delay between the set of 3 burstingpulses. A) Suprathreshold Bursting—15 Pulse. Stimuli consisted of 5bursts. The inter pulse delay between each of the three pulses in eachburst varied between 0.075-32.4 ms. For the 32.4 ms inter pulse delay,the pulses were evenly distributed throughout the 500 ms time period ofstimulation. This inter pulse delay is represented on the x-axis on logaxes. The y-axis is the current needed to reach visual threshold. (B)Suprathreshold Bursting—30 Pulse. Stimuli consisted of 10 bursts. Theinter pulse delay between each of the three pulses in each burst variedbetween 0.075-15.75 ms, with the pulses evenly distributed throughoutthe 500 ms time period of stimulation for the 15.75 ms inter pulsedelay. (C) Suprathreshold Bursting—60 Pulse. Stimuli consisted of 20bursts. The inter pulse delay between each of the three pulses in eachburst varied between 0.075-7.425 ms, with the pulses evenly distributedthroughout the 500 ms time period of stimulation for the 7.425 ms interpulse delay.

Referring to FIG. 26 Model predictions of threshold for a 500 ms pulsetrain for a typical electrode. In each panel the x-axis represents pulsewidth on a logarithmic axis, and the y-axis represents frequency. Reddashed lines represent a current amplitude limit of 200□□mps, yellowdashed lines represent the constraint that stimulation must occur abovethe critical flicker frequency of 50 Hz, and blue dashed lines representthe constraint of a charge density limit of 0.35mC/cm². Light shadingrepresents pulse widths and frequencies that fall outside theseconstraints. The z-axis represents (A) current, (B) charge density, and(C) overall charge across the entire pulse train. Given these exampleconstraints, our model predicts that the most charge efficientstimulation pattern is a 50 Hz pulse train consisting of 0.089 mspulses, as shown by a * in Panel C.

In summary, a process for designing an apparatus and a method forstimulating neural tissue is provided. The apparatus provides a meansfor adjusting the RF link to the internal coils, and the method providesthe maximum intensity with minimum current by modeling responses tovarying stimulation parameters including frequency, pulse width, andpattern of pulse series (trains).

Accordingly, what has been shown is an apparatus and method forstimulating neural tissue for improved response to brightness. While theinvention has been described by means of specific embodiments andapplications thereof, it is understood that numerous modifications andvariations could be made thereto by those skilled in the art withoutdeparting from the spirit and scope of the invention. It is therefore tobe understood that within the scope of the claims, the invention may bepracticed otherwise than as specifically described herein.

What is claimed is:
 1. A visual stimulation method, comprising:generating a first series of stimulation patterns by stimulating neuraltissue of a patient with a series of impulsive electrical signals withvarying stimulation amplitude; determining a relationship of stimulationamplitude to induced phosphene brightness in response to said firstseries of stimulation patterns; generating a second series stimulationpatterns by stimulating neural tissue of a patient with a series ofimpulsive electrical signals, wherein said second stimulation patternalters frequency; predicting how induced phosphene brightness depends onthe second series of stimulation patterns by estimating perceptualthreshold as an exponential function of stimulation frequency versusstimulation amplitude based on stimulation with a time constant of lessthan 1 ms; and altering further stimulation amplitude and frequencybased upon a prediction derived from the step of predicting.
 2. Themethod of claim 1, wherein said first and second series of stimulationpatterns include biphasic pulses with a pulse width that varies between0.075 ms and 4 ms.
 3. The method of claim 1, wherein said determining arelationship of stimulation amplitude to induced phosphene brightnesscomprises evaluating stimulation amplitude to reach perceptual thresholdas a function of pulse width to find that stimulation amplitude to reachperceptual threshold decreases as pulse duration increases.
 4. Themethod of claim 3, wherein pulse width is made variable between 0.075 msand 4 ms.
 5. The method of claim 3, further comprising a delay betweenpulses, wherein said delay is variable and said variable delay variesbetween 0.075 ms and 300 ms.
 6. The method of claim 1, wherein saiddetermining a relationship of stimulation amplitude to induced phosphenebrightness comprises applying a leaky integrator model.
 7. The method ofclaim 1, wherein said determining a relationship of stimulationamplitude to induced phosphene brightness comprises evaluating summationacross at least on pulse pair in function of stimulation amplitude toreach perceptual threshold to determine how a first pulse of the atleast one pulse pair contributes to a perceptual threshold response of asecond pulse of the at least one pulse pair.
 8. The method of claim 1,wherein said determining a relationship of stimulation amplitude toinduced phosphene brightness comprises applying a linear filter to saidfirst series of stimulation patterns, measuring a perceptual threshold,and comparing said perceptual threshold with a predicted perceptualthreshold response based upon said frequency.
 9. The method of claim 1,wherein said a relationship of stimulation amplitude to inducedphosphene brightness comprises applying a non-linear filter to saidfirst second series of stimulation patterns, measuring a perceptualthreshold, and comparing said perceptual threshold with a predictedperceptual threshold response based upon said frequency.
 10. The methodof claim 1, wherein said determining a relationship of stimulationamplitude to induced phosphene brightness comprises applying a linearfilter to said first and second series of stimulation patterns,measuring a non-linearity in a signal resulting from said step ofapplying a linear filter to said first and second series of stimulationpatterns, and comparing said non-linearity with a predicted responsebased upon said frequency.
 11. The method of claim 1, wherein saiddetermining a relationship of stimulation amplitude to induced phosphenebrightness comprises applying a first linear filter o said first andsecond series of stimulation patterns, measuring a non-linearity in asignal resulting from said step of applying a linear filter to saidfirst and second series of stimulation patterns, applying a secondlinear filter, measuring a perceptual threshold, and comparing saidperceptual threshold with a predicted response based upon saidfrequency.
 12. The method of claim 11, wherein said second linear filteris convolved with said measured non-linearity.
 13. The method of claim1, wherein the determining a relationship of stimulation amplitude toinduced phosphene brightness comprises evaluating amplitude to reachperceptual threshold in function of pulse train frequency to find thatcurrent amplitude to reach perceptual threshold decreases as pulse trainfrequency increases.
 14. The method of claim 13, further comprisingevaluating whether decrease of stimulation amplitude to reach perceptualthreshold also depends on number of pulses.
 15. The method of claim 13,wherein said evaluating stimulation amplitude to reach perceptualthreshold in function of pulse train frequency comprises evaluatingplural pulse trains.
 16. The method of claim 15, wherein the pluralpulse trains comprise a first pulse train with two pulses, a secondpulse train with three pulses, and a third pulse train with fifteenpulses.
 17. The method of claim 16, further comprising a delay betweenpulses of each pulse train wherein the delay varies between 0.075 ms to300 ms.
 18. The method of claim 16, wherein at a pulse train frequencyof less than 50 Hz, the perceptual threshold depends on a delay betweenpulses.
 19. The method of claim 1, wherein stimulating neural tissue isstimulating visual neurons.